Florens, Jean-Pierre, Fève, Frédérique and Simar, Léopold (2025) Reconciling Engineers and Economists: the Case of a Cost Function for the Distribution of Gas. TSE Working Paper, n. 25-1640, Toulouse

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Abstract

The analysis of cost functions is an important topic in econometrics both for scientific
studies and for industrial applications. The object of interest may be the cost of
a firm or the cost of a specific production, in particular in case of a proposal to a procurement.
Engineer methods evaluate the technical cost given the main characteristics
of the output using the decomposition of the production process in elementary tasks
and are based on physical laws. The error terms in these models may be viewed as
idiosyncratic chocs. The economist usually observes ex post the cost and the characteristics
of the product. The difference between theoretical cost and the observed one
may be modeled by the inefficiency of the production process. In this case, econometric
models are cost frontier models. In this paper we propose to take advantage of the
situation where we have information from both approaches. We consider a system of
two equations, one being a standard regression model (for the technical cost function)
and one being a stochastic frontier model for the economic cost function where inefficiencies
are explicitly introduced. We derive estimators of this joint model and derive
its asymptotic properties. The models are presented in classical parametric approach,
with few assumptions on the stochastic properties of the joint error terms. We suggest
also a way to extend the model to a nonparametric approach, the latter provides an
original way to model and estimate nonparametric stochastic frontier models. The
techniques are illustrated in the case of the cost function for the distribution of gas in
France.